A392503 Number of partitions of [n] having exactly one block size whose multiplicity equals its size.

0, 1, 0, 3, 7, 5, 111, 497, 876, 9361, 57280, 276232, 1493911, 13307021, 81816840, 553023200, 3525335365, 37183142815, 286940599516, 2528236631758, 17444588118460, 198002457036930, 1819149646834784, 19317014599504327, 169445645840969537, 1836754417373853251

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Wikipedia, Partition of a set

Example

a(4) = 7: 12|34, 13|24, 14|23, 1|234, 134|2, 124|3, 123|4.

Maple

b:= proc(n, i, t) option remember; uses combinat; `if`(n=0, t,
     `if`(i<1, 0, add(`if`(i=j and t=1, 0, b(n-i*j, min(n-i*j, i-1),
     `if`(i=j, 1, t))*multinomial(n, n-i*j, i$j)/j!), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..25);

Crossrefs

Cf. A000110, A391611.

Sequence in context: A277207 A380170 A001663 * A085052 A218363 A200611

Adjacent sequences: A392500 A392501 A392502 * A392504 A392505 A392506

Keyword

nonn

Author

Alois P. Heinz, Feb 21 2026

Status

approved